Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#456 ⋊ C2 |
| Sylow | C5 ⋊ #3022 |
704 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,e^c=eg,h^c=h^4,h^d=h^461 conjugacy classes — view the full character table.
| maximal subgroup of | #12253504, #12253506, #12253511, … |
| maximal normal subgroup of | #12253504, #12253506, #12253511, … |
| maximal quotient of | #12071700, #12071731, #12071776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 14113);